Find the number of degree of freedom (to the nearest integer ) of molecule of gas, whose molar heat capacity is C=29J/mol/K (in the process PT= constant) .
Question
Find the number of degree of freedom (to the nearest integer) of molecule of gas, whose molar heat capacity is C=29 J/mol/K (in the process PT= constant).
Solution
To find the number of degrees of freedom of a molecule of gas, we can use the equation:
C = (f/2)R
where C is the molar heat capacity, f is the number of degrees of freedom, and R is the gas constant.
In this case, we are given that C = 29 J/mol/K. The gas constant R is approximately 8.314 J/mol/K.
Substituting these values into the equation, we have:
29 = (f/2) * 8.314
To solve for f, we can rearrange the equation:
f/2 = 29 / 8.314
f/2 ≈ 3.49
Multiplying both sides by 2, we get:
f ≈ 6.98
Since the number of degrees of freedom must be an integer, we round f to the nearest whole number.
Therefore, the number of degrees of freedom of the molecule of gas is approximately 7.
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